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Omni-MATH / Let k be a positive integer. Lexi has a dictionary D consisting of some k-letter strings containing only the letters A and B. Lexi would like to write either the letter A or the le…

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problem

Let kk be a positive integer. Lexi has a dictionary D\mathbb{D} consisting of some kk-letter strings containing only the letters AA and BB. Lexi would like to write either the letter AA or the letter BB in each cell of a k×kk \times k grid so that each column contains a string from D\mathbb{D} when read from top-to-bottom and each row contains a string from D\mathbb{D} when read from left-to-right. What is the smallest integer mm such that if D\mathbb{D} contains at least mm different strings, then Lexi can fill her grid in this manner, no matter what strings are in D\mathbb{D}?
Plain-text mathematical notation (without MathML)
Let k be a positive integer. Lexi has a dictionary D consisting of some k-letter strings containing only the letters A and B. Lexi would like to write either the letter A or the letter B in each cell of a k×k grid so that each column contains a string from D when read from top-to-bottom and each row contains a string from D when read from left-to-right. 
What is the smallest integer m such that if D contains at least m different strings, then Lexi can fill her grid in this manner, no matter what strings are in D?
Original LaTeX notation
Let $k$ be a positive integer. Lexi has a dictionary $\mathbb{D}$ consisting of some $k$-letter strings containing only the letters $A$ and $B$. Lexi would like to write either the letter $A$ or the letter $B$ in each cell of a $k \times k$ grid so that each column contains a string from $\mathbb{D}$ when read from top-to-bottom and each row contains a string from $\mathbb{D}$ when read from left-to-right. 
What is the smallest integer $m$ such that if $\mathbb{D}$ contains at least $m$ different strings, then Lexi can fill her grid in this manner, no matter what strings are in $\mathbb{D}$?

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Source and history

task_id
771292b2-e788-5126-ac26-3f4c4c467e9c
task_key
test--771292b2-e788-5126-ac26-3f4c4c467e9c
task_revision_id
1
config / split
/ test

Official source

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